Ireland downed Hong Kong by 85 runs for their seventh successive victory while Afghanistan defeated Kenya by 34 runs, giving the Asian side their sixth win in seven matches.
Sunday's results mean Ireland and Afghanistan have topped their respective groups and, as such, have qualified automatically for the event proper.
This is Ireland's fourth successive qualification for the ICC World Twenty20 after participating in the 2009, 2010 and 2012 editions, whereas for Afghanistan, it will be the third time.
With four places in the ICC World Twenty20 Bangladesh 2014 still up for grabs, Hong Kong will face Nepal and the United Arab Emirates (UAE) will square off against the Netherlands Wednesday.
The two winners will also qualify for the Bangladesh event that will be staged from March 16 to April 6.
Also Wednesday, Namibia will take on Papua New Guinea (PNG) and Scotland will face Italy.
The winners of Namibia-PNG and Scotland-Italy matches will lock horns against the losers of Hong Kong-Nepal and UAE-Netherlands matches Thursday, with the two winners completing the line-up of the six qualifiers for the ICC World Twenty20 Bangladesh 2014.